If you are keen to learn, get to grips with something with the willing help of one of the net's original musician forums or possess a genuine willingness to contribute knowledge - you've come to the right place!

If this is your first visit, be sure to
check out the FAQ by clicking the
link above. You may have to register
before you can post: click the register link above to proceed. To start viewing messages,
select the forum that you want to visit from the selection below.

Ascending substitute dominants

If I use a substitute dominant ascending, should it be notated as a #?
So, Dm7-Db7-CM7 is fine. Should the ascending form be spelled CM7-Db7-Dm7 or CM7-C#7-Dm7?

If it were a °7 I would expect CM7-C#°7-Dm7. But substitute dominants are defined by their expectation to resolve down a semitone. They are, in some way, inherently flat. Are they still flat when that expectation is confounded?

Finally a few observations about PCS theory -
Forte's work, while groundbreaking, reveals the thinking of a mathematician rather than a musician. Specifically in its treatment of mirror sets (inversions) and its ordering.
In Forte's work inversions are treated as identical. This leads to the situation that, for instance, the major and minor triads come from the same set (3-11) and the Harmonic minor and Harmonic major are both from (7-32). Later work has "corrected" this and now the inversions are separated, so the minor triad comes from 3-11a and the major from 3-11b. Likewise Harmonic minor is 7-32a, Harmonic major 7-32b.
The other problem is that the sets are arranged into an order which makes little sense to a musician.
The Diatonic scale is 7-35. Melodic minor is 7-34. 7-33 has no common name. 7-32a is Harmonic minor, 7-32b is Harmonic major. z-related sets can be miles apart in the lists.

So I sorted them all by maximal evenness and, almost magically, the common sets float to the top. Not really magical, evenness is a powerful indicator of utility in both chords and scales.
Here's the map... http://chordspace.com/images/jpegs/Map3.jpg

I'll be fascinated to hear it. As a software writer it informs everything I do. Other theorists have used it to good effect to interpret existing scores. What I haven't yet heard is much music which explicitly leverages it for composition.
And I'm a great believer that "There's nothing as practical as a good theory".

"There are only (208) prime forms, I took two days and played everyone of 'em on the piano"

Why? The prime forms are likely to be the least interesting rotations. I'd be playing the (to coin a phrase) Anti-primes - the least compact rotations.
Locrian is the prime of the Diatonic, Lydian is the Anti-prime.

Whilst from a maths point of view there are 208 prime forms, from a musicians point of view there are 352.
Forte considered chiral sets to be equivalent, musicians don't.
Put simply, for Forte Harmonic Minor and its inversion, Harmonic Major are the same set (7-32) with a prime form of {0,1,3,4,6,8,9}.
For the rest of us these are 2 distinct sets 7-32a (Harmonic Minor, prime {0,1,3,4,6,8,9}) and 7-32b (Harmonic Major, prime {0,1,3,5,6,8,9}).